Answer
See answers.
Work Step by Step
a. The amplitude is the maximum x value, 0.650 m.
b. The frequency is $f = \frac{\omega}{2\pi}$. We see from the problem that $\omega =8.40\;rad/s$ . Solve for f = 1.34 Hz.
c. The total energy is given by the kinetic energy when the speed is highest:
$$E_{total}=\frac{1}{2}mv^2_{max}=\frac{1}{2}m(\omega A)^2$$
$$=\frac{1}{2}(1.15\;kg) ((8.40\;rad/s)(0.650m))^2=17.1\;J$$
d. First find the PE.
$$E_{potential}=\frac{1}{2}kx^2=\frac{1}{2}m\omega^2x^2$$
$$=\frac{1}{2}(1.15\;kg) ((8.40\;rad/s))^2(0.360\;m)^2=5.3\;J$$
The kinetic energy there is the total energy minus the potential energy, or 11.8 J.
